4. [10 marks] Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams, Let I be the event that a student works part time, and ) be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events Wand V. A. [2.5) What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? B. [2.5] What proportion of students do not work part time but are part of one of the university's sports teams? C. [1.5] Are W and I' independent events? D. [1.5) If a student works part time, what is the probability they are also part of one of the university's sports teams? E. [21 What proportion of students are not part of any of the university's sports teams and work part time